What is 9/14 plus 2/3? (Answer: 55/42)

Exact Answer

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Problem: What is 9/14 plus 2/3?
Formula / Expression: 9/14 + 2/3
Final Answer: 1 13/42 (55/42)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 3 = 42.
Working: LCD(14, 3) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 9/14 by 3, and multiply the numerator and denominator of 2/3 by 14 so both fractions share the common base 42.
Working: 9 × 3/14 × 3 = 27/42 and 2 × 14/3 × 14 = 28/42

Step 3: Add the Numerators
Now add the numerators (27 + 28 = 55) and keep the common denominator 42 unchanged.
Working: 27 + 28/42 = 55/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 55 and 42 is 1, confirming that 55/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 55/42

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (55) is greater than the denominator (42), divide 55 by 42: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/42.
Working: 55/42 = 1 13/42

Step 6: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 42 produces a repeating decimal (approximately 1.309524, or 130.9524%).
Working: 55 ÷ 42 = 1.309524 (130.9524%)

Key Values:
- Simplified Fraction: 55/42
- Mixed Number Form: 1 13/42
- Decimal Value: 1.309524
- Percentage: 130.9524%

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Solved with FractionsCalc:
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9/14 + 2/3 = 55/42

Simplified Fraction

55/42

Mixed Number

1 13/42

Decimal Value

1.309524

Percentage

130.9524%

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Step-by-Step Solution: 9/14 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 3 = 42.

LCD(14, 3) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 9/14 by 3, and multiply the numerator and denominator of 2/3 by 14 so both fractions share the common base 42.

9 × 3/14 × 3 = 27/42 and 2 × 14/3 × 14 = 28/42

Step 3

Add the Numerators

Now add the numerators (27 + 28 = 55) and keep the common denominator 42 unchanged.

27 + 28/42 = 55/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 55 and 42 is 1, confirming that 55/42 cannot be reduced further—it is already in its simplest irreducible form.

55/42

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (55) is greater than the denominator (42), divide 55 by 42: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/42.

55/42 = 113/42

Step 6

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 42 produces a repeating decimal (approximately 1.309524, or 130.9524%).

55 ÷ 42 = 1.309524 (130.9524%)

Visual Representation

The diagram below illustrates 9/14 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/42`
Mixed Number Form	`1 13/42`
Decimal Form	`1.309524`
Percentage	`130.9524%`

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Frequently Asked Questions

What is 9/14 plus 2/3 as a fraction?

9/14 + 2/3 in simplest fraction form is 55/42 (or 1 13/42 as a mixed number).

What is 9/14 plus 2/3 as a decimal?

9/14 + 2/3 converted to a decimal is 1.309524.

What is 9/14 plus 2/3 as a percentage?

9/14 + 2/3 expressed as a percentage is 130.9524%.

How do you write 9/14 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 55/42 can be written as the mixed number 1 13/42.

Does 9/14 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.309524...) because the denominator contains prime factors other than 2 and 5.